\(=P_{\text {photon }}=\frac{h v}{c}\)

From the law of conservation of linear momentum, Momentum of recoil nucleus

\(=p_{\text {nucleus }}=p_{\text {photon }}\)

\(\therefore \quad M v=\frac{h v}{c}\)

where \(v\) is the recoil speed of the nucleus or \(\quad v=\frac{h v}{M c}\)  ..... \((i)\)

The recoil energy of the nucleus

\(=\frac{1}{2} M v^{2}=\frac{1}{2} M\left(\frac{h v}{M c}\right)^{2}=\frac{h^{2} v^{2}}{2 M c^{2}} \quad(\text { Using }(\mathrm{i}))\)